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Aug
19
answered Discretization of normal distribution over a finite range
Aug
19
comment Congruence proof of modulus equivalence
Except that the formulation "Without loss of generality" is stylistically not applicable here
Aug
19
answered Proving no finite basis of the system of neighborhoods at $a$ in the real line exist.
Aug
19
answered Question regarding n consecutive positive integers
Aug
18
comment Optimal Number of Entries for a Contest of Skill…
From reading this it does not sound that the "slots" and "variables" and "trdaitionally scoring more" and whatnot have any influence. It seems, You want us to estmiate the distribution of your exact ranking in a random contess based on the sole information that the probabilty that you rank above the median is $0.57$?
Aug
18
comment What is the difference between $\mathbb{N}$, $\mathbb{Z}$ and $\mathbb{Q}$ in terms of their metrics?
What is the usual Euclidean metric on an (arbitrary?) countably infinite set $X$?
Aug
18
comment A better way to prime factorize a set of numbers?
You already meantion that you need only primes up to $\sqrt n$, why do you still generate primes up to $10^9$ or $999824$?
Aug
18
comment A better way to prime factorize a set of numbers?
@ThomasAndrews Actually, optimal is already a superlative, so better is really the best (not to say: optimal) formulation :)
Aug
18
awarded  Nice Question
Aug
18
comment Closed form of solution of recurrence equation
Note that $a_n^2-a_n+1=(a_n-\frac12)^2+\frac34$, hence with $b_n:=a_n-\frac12$ we have $b_{n+1}=b_n^2+\frac14$. This iteration corresponds to the cusp of the Mandelbrot set. If $b_0=\frac12$, the sequence is constant; if $|b_0|<\frac12$ the sequence will converge to $\frac12$; if $b_0>\frac12$ it will diverge. So much for the behaviour as $n\to \infty$. Do you really want $b_n$ (or $a_n$) explicitly?
Aug
18
comment When does $2^n+n \mid 8^n+n$?
If one does not like $\equiv$, one can also write down directly that $(2^n+n)(4^n-2^nn+n^2)=8^n+n^3=(8^n+n)+(n^3-n)$
Aug
18
answered Generate random results in a continuous field
Aug
18
comment Approximation of (n^n)^n
The question is apparently: How good must we approximate the log in order to obtain enough significant digits? Since $n^2$ kills about 20 digits and we want 10 (and log and exp are relatively harmless), we should start by computing $\log_{10}1.23456789$ to about $30$ decimal places ...
Aug
18
answered Latitude and longitude to screen coordinates using “mapping points”?
Aug
18
comment How inequalities are made
In the case of contest math, it is often the other way round: You start with a well-known inequality and make a clever transformation away from it. So the problem inequalities are not conjectured and then proved, they are hand-crafted for the contest right away. (I know what I am talking about: Long ago, during my own training for the IMO, in one of the training lectures we were shown some very nice examples of how to create intriguing inequality problems from simple standard iniequalities)
Aug
17
answered Prove that $\lim_{x\to\infty}f''(x)=0$ if $\lim_{x\to\infty}f(x)=T$ and $\lim_{x\to\infty}f'''(x)=0$.
Aug
16
answered Usage of the term “Free”
Aug
15
comment Mersenne Numbers 1+4k
+1 for this surprisingly direct method.
Aug
15
comment How prove this $Z(H)\neq 1$, if for any $g\in G\setminus H, H\cap H^g=1$
Is "for any" = "for every" or "for some"?
Aug
14
reviewed Leave Closed A Question about Doctoral Theses in Mathematics